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Journal of Process Control 24 (2014) 113–124

Contents lists available at ScienceDirect

Journal of Process Control

j ourna l ho me pa ge: www.elsev ier .com/ locate / jprocont

ynamics and control of benzene hydrogenation via reactiveistillation

ishal Mahindrakara, Juergen Hahna,b,∗

Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United StatesDepartment of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States

r t i c l e i n f o

rticle history:eceived 14 October 2013eceived in revised form 3 January 2014ccepted 7 January 2014vailable online 28 February 2014

eywords:

a b s t r a c t

This work develops a dynamic, first principles-based model of a reactive distillation column used for ben-zene hydrogenation of a reformate stream and investigates different control structures for this process.The model is used initially to develop and evaluate a feedback control strategy which provides good reg-ulatory performance for small disturbances, however, it tends to be sluggish for significant disturbancesin the feed composition. In order to address this point, adding a feedforward controller to the feedbackstructure has also been investigated. However, the feedforward controller can only be implemented if

eactive distillationacked columnynamic modelingeedback controleedforward control

composition measurements of the feed are taken. As online composition measurements are expensivein practice, several different scenarios have been investigated where samples of the feed are taken andsubsequently analyzed in a lab, as represented by measurement time delays. Simulation results showthat adding feedforward control to the feedback scheme can be very beneficial for this process, however,this is only the case if the composition disturbance measurements do not involve a significant time delay.

. Introduction

Automotive emissions are a significant contributor to poor airuality [1]. As such, specifications for automobile fuels obtainedrom petroleum have received increasing levels of attention fromhe Environmental Protection Agency (EPA). Benzene is one of theompounds that is regulated as it is a carcinogen and the EPAequires all refiners to limit the amount of benzene in gasoline to.62 vol% [2]. While benzene in the gasoline pool results from a vari-ty of sources, the main contributor is the reformer unit resultingn significant amounts of benzene present in reformate streams.s the reformate stream is used to boost octane rating, there areconomic objectives that have to be taken into account while com-lying with environmental regulations.

One option to remove benzene is to hydrogenate in the presencef a catalyst. However, a problem arises as the catalyst used forhe reaction is not exclusively selective for benzene, and toluene,hich is present in the reformate stream in considerable quantities,

ill also be hydrogenated. Toluene hydrogenation is undesirable as

∗ Corresponding author at: Center for Biotechnology and Interdisciplinary Studies,ensselaer Polytechnic Institute, Troy, NY 12180, United States.el.: +1 518 276 2138; fax: +1 518 276 3035.

E-mail address: hahnj@rpi.edu (J. Hahn).

959-1524/$ – see front matter © 2014 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.jprocont.2014.01.005

© 2014 Elsevier Ltd. All rights reserved.

toluene has a high octane rating (RON) and should be retained inthe final product.

Benzene (100 RON) + 2H2 → cyclohexane (83 RON) (1)

Toluene (120 RON) + 3H2 → methylcyclohexane (75 RON) (2)

In order to avoid problems related to the selectivity of the cata-lyst, the reformate stream is split into light and heavy componentsin the conventional process (Fig. 1a). As benzene is a reasonablylight component of this mixture, it is mostly concentrated in thedistillate, and accordingly, is hydrogenated before being sent tothe gasoline pool. The downside of this process is that a high cap-ital investment is needed. Reactive distillation (Fig. 1b) offers analternative route for solving this problem. By combining reactionwith separation it is possible to selectively react one component ina specified region of the column while suppressing unwanted reac-tions of other components. Furthermore, additional savings can beachieved as the heat of reaction can directly be used for separationof the mixture.

While reactive distillation (RD) can have significant advantagesover traditional designs, there are also challenges that needto be considered. The simultaneous presence of reaction andseparation phenomena can result in complex dynamic behavior.

Combining reaction and separation into a single vessel results infewer manipulated variables, thus increasing interactions betweencontrol loops [3]. RD columns have been observed to be verysensitive to changes in feed concentration. This is a crucial aspect

114 V. Mahindrakar, J. Hahn / Journal of Pro

Notation

a geometric surface area of packing per unit volume(m2 m−3)

A cross sectional area of columnCA concentration (mol m−3)dp packing particle diameter (m)ds column diameter (m)D distillate flow rate (mol s−1)Ea reaction activation energy (J mol−1)F feed flow rate (mol s−1)hi total liquid holdup based on empty column

(m3 m−3)Hlj molar enthalpy of liquid stream on stage j (J mol−1)

Hvj molar enthalpy of vapor stream on stage j (J mol−1)HETP height equivalent to a theoretical stage (m)k reaction rate constant (mol s−1 kg−1)K wall factorKA reaction adsorption coefficient (m3 mol−1)

KH reaction adsorption coefficient (m3 mol−1)L liquid flow rate (mol s−1)M mass holdup (kg)Mlj liquid molar holdup on stage j (mol)Mvj vapor molar holdup on stage j (mol)N number of stagesP pressure (Pa)�P0,j dry column pressure drop across stage j (Pa)�Pj irrigated column pressure drop across stage j (Pa)Q external heat energy input (J)R reflux ratioRgas gas constant (J mol−1 K−1)Rev vapor Reynolds numberrxn reaction rate (mol s−1 kg−1)s Laplace variableT0 reaction reference temperature (K)Tj temperature on stage j (K)V vapor flow rate (mol s−1)u specific liquid load (m s−1)x liquid mole fractiony vapor mole fractiony* equilibrium vapor mole fractionz feed mole fraction

Greek lettersε packing void fraction�lj,i liquid fugacity coefficient of component i on stage j�vj,i vapor fugacity coefficient of component i on stage j

�cat catalyst density (kg m−3)� Murphree efficiency� relative gain� relative gain array transfer function time constant (s)c controller design parameter (s) transfer function time delay (s) resistance coefficient

Subscripts

fmda

i component indexj stage index

or benzene hydrogenation as the concentration of some of theain components in the feed can vary by 50% or more due to

isturbances upstream from the column [4]. The importance ofddressing these disturbances is increased by the fact that changes

cess Control 24 (2014) 113–124

in the feed happen on a daily basis and a column operating under afeedback control can take several hours to return to an acceptablesteady states. This paper investigates these points by developinga detailed dynamic model, studying the dynamic behavior insimulations, and developing a control scheme. Furthermore, thepossibility of implementing a feedforward control scheme, inaddition to a feedback one, is investigated where it is taken intoaccount that feed composition measurements may involve timedelays if the measurements are taken as samples analyzed in a lab.

The outline of this paper is as follows. A literature review ispresented in the following subsection and Section 2 presents pre-liminary information. A detailed description of the model andcontrol structure is presented in Section 3. Section 4 discusses col-umn responses to a series of commonly occurring disturbances.Conclusions are given in Section 5.

1.1. Literature review

Reactive distillation has received a lot of attention as part ofprocess intensification efforts in the last couple of decades. Employ-ing reactive distillation can result in energy savings as the heat ofreaction is directly used for separation of the mixture. Harmsen[3] has reviewed commercial applications of reactive distillation.Reactive distillation systems have been shown to reduce variablecost, capital expenditure and energy requirements by 20% or morefor some processes [3]. Also, since the heat of reaction is used forevaporation in a column, increased reaction rates can results inincreased evaporation rates without significant changes of the tem-perature. Thus, reactive distillation columns have been found tobe less susceptible to runway behavior than conventional reactors[3]. Reactive distillation models have been surveyed extensively byTaylor and Krishna [5] and several articles describing dynamic mod-els, and control structures [6–9] are available. A variety of differentapplications of reactive distillation in refineries have been reported,such as processes involving ethers (MTBE, ETBE, and TAME [10]).Sneesby et al. [11–13] have developed dynamic models for ETBEand MTBE, and also made general recommendations for controlsystem design. Different control strategies for MTBE reactive dis-tillation columns were highlighted by Bartlett and Wahnschafft[14]. A number of authors have also explored the dynamics andcontrol for reactive distillation of TAME [15–18]. However, despitethese extensive efforts on reactive distillation in general, no paperson benzene hydrogenation via reactive distillation can be foundin the open literature. This situation is especially peculiar as ben-zene hydrogenation is an important step in a refinery and severalRD columns used for benzene hydrogenation are in operation inrefineries throughout the world.

2. Preliminaries

This section reviews preliminary information needed for theremainder of the paper. Section 2.1 reviews existing modelingapproaches for reactive distillation columns, some of which willbe used in this work. Existing control strategies for reactive dis-tillation columns are discussed in Section 2.2.1 and Section 2.2.3reviews the principles of feedforward control which will also beused.

2.1. Packed column modeling

Reactive distillation can be viewed as an extension of con-ventional packed columns, where some of the packing includes a

catalyst to facilitate a reaction taking place. A number of papershave discussed modeling of conventional packed columns. Thekey methods used for packed columns are equilibrium (EQ) stagemodeling and non-equilibrium stage modeling (NEQ). In EQ stage

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124 115

n/sep

mltNMr[tahcBqfi[o

erismTdhAuaftapuhp

2

2

aslps

of controlled variables used. Eq. (3) presents the set of manipulatedvariables u and controlled variables y that are used in 5 × 5 systemsin no particular order of correlation; see Fig. 2 for an illustrationof the variables. Columns having a 4 × 4 control system frequently

Fig. 1. Schematics of (a) conventional reactio

odels, the vapor and liquid phase are assumed to be in equi-ibrium. NEQ stage models use rate-based equations to describehe mass transfer occurring in conventional distillation columns.EQ stage models are generally based on the use of rigorousaxwell–Stefan equations for estimating heat and mass transfer

ates across the interface. Many papers have presented EQ models6,8,12,13,19–21] and NEQ models [16,17,20–22] for reactive dis-illation. Most of the NEQ models developed for reactive distillationre generally steady state models [20–22]. However, Peng et al. [23]ave compared the results of dynamic NEQ and EQ model, and con-luded that the results are similar for their case. Contrary to this,aur [17] pointed out that the responses from the models may differuantitatively and the dynamics are influenced by column speci-cations. NEQ models are generally more challenging to simulate17,23] and require thermodynamic properties for the calculationf mass transfer coefficients and interfacial areas.

The dynamic behavior of a distillation column is strongly influ-nced by fluid hydraulics in the column. This is even more so ineactive distillation columns, as liquid hold-ups, and liquid res-dence times are important for determining the conversion andelectivity of the reactive distillation column. Very few dynamicodels consider both liquid and vapor holdup in the columns.

he vapor holdups are generally neglected because of the lowensity of vapor in comparison to liquid. Also, considering vaporoldups leads to additional computational difficulties in the model.s such, most dynamic models consider only dynamic liquid holdp or in some cases a constant liquid holdup [23]. However, Choend Luyben [24] suggest that vapor holdup should be consideredor dynamic models of columns operating at pressures greaterhan 5–10 atm. Equations governing the vapor and liquid flows,nd hold-ups in a packed column have been discussed by manyapers: Bemer and Kalis [25] have given equations for liquid hold-p and pressure drops in irrigated columns while Mackowiak [26]as extensively reviewed methods for determining vapor flow inacked columns.

.2. Control structure

.2.1. Feedback controlReactive distillation columns are systems with multiple inputs

nd multiple outputs (MIMO). One approach to deal with MIMO

ystems is to treat the control problem as separate individualoops, i.e., assume that each manipulated variable affects only onearticular controlled variable and design a controller for each loopeparately. This type of control structure is also referred to as a

aration process and (b) reactive distillation.

multi-loop control system [27]. A major concern with multi-loopcontrol is the presence of process interactions, i.e., each manipu-lated variable may affect multiple controlled variables, however,these interactions are not taken into account for the controlstructure design. Multi-loop control systems may not providesatisfactory control in some scenarios and multivariable controlstrategies, such as model predictive control and decoupling controlcan provide better control. However, multi-loop control is themost widely used control strategy for distillation columns becauseof its simplicity, both in terms of maintenance and controllertuning. As no work has been done on modeling and control ofbenzene hydrogenation via reactive distillation, this work focuseson traditional control strategies and advanced control will beinvestigated in the future.

The commonly used control structures for reactive distillationare similar to those of conventional distillation columns. Skogestadand co-workers [28–30] have discussed the selection of controlledand manipulated variables. Most distillation columns generally useeither a 4 × 4 control or a 5 × 5 control structure. These configura-tions refer to the number of manipulated variables and the number

Fig. 2. Conventional distillation column.

1 l of Pro

dv

u

wctlaauaeawtc

tsinccpscpftaflpflicadbsa

2

iIaptacy

�

16 V. Mahindrakar, J. Hahn / Journa

o not use the pressure at the top of column, P1, as a controlledariable [30].

=

⎛⎜⎜⎜⎜⎜⎜⎝

L1

VN, QN

D

LN

V2, QD

⎞⎟⎟⎟⎟⎟⎟⎠

y =

⎛⎜⎜⎜⎜⎜⎜⎝

x1

xN

M1

MN

P1

⎞⎟⎟⎟⎟⎟⎟⎠

(3)

The 5 × 5 system shown in Fig. 2 is generally used for columnsith a total condenser. For these columns, the pressure is typi-

ally controlled by manipulating the condenser heat removal ashe condenser temperature and the column pressure are directlyinked for a total condenser. Partial condensers are used when therere very light components in the column feed that would require

high column pressure or a low condenser temperature. In a col-mn with a partial condenser, vapor is removed from the condensers a vapor stream. The pressure of the column is strongly influ-nced by the outlet vapor stream flow rate. Luyben [31] and Horind Skogestad [32] have discussed control structures for columnsith partial condensers. Sloley [33] has extensively reviewed con-

rol strategies that can be used for columns based on the type ofondenser.

Recycle loops in chemical plants are known to significantly alterhe control and dynamics of process networks [34–36]. Recycletreams increase the overall time constants, thus “slowing down”ts overall response [34]. Designing a control structure for processetworks with recycle can be challenging because recycle streamsan induce a time scale separation, where the dynamics of the pro-ess evolves at a fast time scale, and the dynamics of the overallrocess with recycle at a slower time scale [37]. Dynamical analy-is and control of such process networks with recycle have receivedonsiderable attention [37]. One of the first design procedures wasroposed by Buckley [38] and has been widely used in industryor many years [39]. The first step is to design a control struc-ure that handles the inventory of the entire process (liquid levelsnd gas pressures). This “hydraulic” structure provides smoothow rate changes. Fast-acting proportional-only level controllersrovide the most simple and most effective way to achieve thisow smoothing [39]. The second step is to close the “product qual-

ty” loops. These loops typically use slower proportional–integralontrollers to hold product streams as close to the specifications possible. Larsson and Skogestad [40] and Luyben et al. [41] haveiscussed plant-wide controller design procedures for a large num-er of measurements and control loops. When applied to a smalleringle unit scale, they mirror the steps that have been mentionedbove.

.2.2. Relative gain arrayAn important general problem for a multi-loop control structure

s to pair the controlled variables and the manipulated variables.ncorrect pairing may result in poor control performance and inter-ctions among controlled variables. One way to determine theairing is Bristol’s relative gain array (RGA) [42]. Bristol developedhe RGA as a systematic approach to measure the process inter-ctions and recommend an effective pairing of manipulated andontrolled variables. The relative gain between a controlled variablei and manipulated variable uj is defined as follows [27]:

ij �(∂yi/∂uj)u(∂yi/∂uj)y

= open-loop gainclosed-loop gain

(4)

cess Control 24 (2014) 113–124

The relative gains are arranged to form the matrix

� =

⎡⎢⎢⎢⎢⎣

�11 �12 · · · �1n

�21 �22 · · · �2n

......

......

�n1 �n2 · · · �nn

⎤⎥⎥⎥⎥⎦ (5)

Controlled and manipulated variables are paired such that thecorresponding relative gains are positive and as close to one aspossible. While the above definition of RGA may seem difficult toestimate directly for real systems, the RGA can be determined froman open-loop gain matrix. The procedure for computing the RGAfrom an open-loop gain matrix, K, is given by

H = (K−1)T

(6)

� = K ⊗ H (7)

where ⊗ denotes the Schur product (element by element multipli-cation) [27].

The controllers used for feedback control loops are generallycontrollers of PID-type, where PI controllers are the most com-monly used ones. Luyben [31] has pointed out that flow controllersthat regulate the inventory of a column, e.g., the distillate and bot-tom flow, should be proportional-only controller as the inventoryin the column is sufficiently large to overcome the effect of offsetsthat may occur due to the use of proportional-only controllers.

2.2.3. Feedforward controlFeedback control does not take corrective action until after

deviations in the controlled variables occur. As the effects of feeddisturbances will only be detected after a while, this lack of predic-tive control can limit the overall column performance, especially ifthe column includes large time constants or time delays. One optionis to also include feedforward control in addition to feedback con-trol in a control structure. Feedforward control systems measurethe disturbance variables and take corrective action before upsetsof the controlled variables can be recorded. The main disadvan-tage of feedforward control is that the disturbance variable mustbe measured online which is not always feasible, physically or foreconomic reasons.

The basic idea for feedforward controller is to measure thedisturbance affecting the system and compute a change of themanipulated variable such that the effect of the disturbance onthe controlled variable is canceled by the change of the manipu-lated variable [44]. Feedforward controller designs are thus basedon process models. A feedforward controller transfer function Gffor a system can be given by [27]

Gf = − GdGpGmf

(8)

where Gd is the disturbance transfer function, Gp is the processtransfer function, and Gmf is the disturbance sensor/transmittertransfer function. Sometimes modifications to the control lawshown in Eq. (8) need to be made to ensure that the resultingcontroller is realizable [27].

Often, the dynamics between a process and a disturbanceare neglected and a simple static feedforward controller may bedesigned if the responses are satisfactory. A static feedforward con-troller is given by the ratio of gains of disturbance, process, andmeasurement transfer functions [44]

Gf = − KdKpKmf

(9)

where Kd, Kp, and Kmf are gains of the disturbance, process, andmeasurement transfer functions.

V. Mahindrakar, J. Hahn / Journal of Pro

Table 1Feed composition for the RD column.

Component Mole fraction

n-Butane C4H10 0.0126n-Pentane C5H12 0.09612,3-Dimethylpentane C7H16 0.01163-Methylpentane C6H14 0.0587n-Hexane C6H14 0.0350Benzene C6H6 0.0826Cyclohexane C6H12 0.00003-Methylhexane C7H16 0.02332,4-Dimethylpentane C7H16 0.0234n-Heptane C7H16 0.0098Toluene C7H8 0.2814m-Xylene C8H10 0.2063Cumene C9H12 0.1594Hydrogen H2 0.0000

mcbfp

3

3

ambpianiuThitffsocpa

udkbiabapTtldm

Methylcyclohexane C7H14 0.0000

Feedforward control depends on the accuracy of the disturbanceeasurement and on the accuracy of the model describing the pro-

ess. As some inaccuracies cannot be avoided, feedforward controly itself would often result in an offset. As a consequence, feed-orward control is commonly combined with feedback control inractice [43].

. RD column design and control

.1. Development of dynamic model

The RD column used in this benzene hydrogenation study is packed column with a throughput of 200,000 lb/h. The refor-ate stream enters the column as feed which is processed into

enzene-free lights and heavy stream. The feed stream has 15 com-onents that need to be modeled and the feed composition is given

n Table 1. The column has 70 theoretical stages which includes partial condenser and a reboiler. The column stages have beenumbered from top to bottom in this investigation. The first stage

s the reflux drum and the last stage is the reboiler drum. The col-mn model has 10 catalyst stages at the top, i.e., stage 2–stage 11.he feed to the column is added at stage 30. The reformate streamas a nominal benzene concentration of 6.0 vol% which is common

n refineries [4]. It is expected that the feed benzene concentra-ion may be as high as 11.0 vol% [4]. Hydrogen to the column ised at stage 29 along with the unreacted hydrogen that is recycledrom the partial condenser. The column is required to meet EPApecification of 0.62 vol% maximum benzene concentration at theutlet during regular operation. Note that the outlet benzene con-entration throughout this investigation refers to the total volumeercentage (vol%) taken over all the liquid streams (both distillatend bottom) exiting the unit.

The RD column is a packed column where a section of the col-mn is filled with catalyst. Industrial data regarding the packingetails and type of catalyst used are unavailable as these are usuallyept a trade secret. Also, no publications on reactive distillation forenzene hydrogenation are available in the open literature. Thus,

n the absence of any sort of information regarding the packing, standard packing size (25 mm pall rings) and catalyst size haseen used in this work. The packing has been treated as equiv-lent to theoretical trays and a height equivalent to theoreticalacking (HETP) of 0.45 m has been used throughout the column.he diameter of the column has been determined by assuming

hat the vapor velocity reaches a maximum of 80% of the floodingimit [26]. Based on the vapor flow estimated in the column, theiameter of the column was estimated to be 2.8 m. Two differentodeling methods are commonly used for each stage of a column:

cess Control 24 (2014) 113–124 117

equilibrium-based (EQ) stages and non-equilibrium-based (NEQ)stages. NEQ models include more detail, but some of the modelparameters are usually not well known and it is unclear if NEQmodels provide a more accurate description than EQ-based mod-els. As such an equilibrium-based modeling approached is usedin this work. Reaction kinetics for the catalyst section have beentaken from Toppinen et al.’s [45] work on hydrogenation of ben-zene and other alkyl benzenes. Benzene hydrogenation columnsoperate at a relatively high pressure of 8 atm, and hence variablevapor holdups have been taken into account. Also, the feed streamhas 15 components that need to be modeled, and some of thesecomponents are bound to have low concentrations in some stagesof column. If a dynamic model considers no vapor hydraulics, thenthe vapor flow rates are also dependent on the molar balances. Thiscreates a problem for the initialization of the model, as the stark dif-ferences in the concentration of individual components may leadto inaccurate estimation of flow rates. In the presence of vaporhydraulics, the vapor flow rates are governed by the hydraulicsfacilitating initialization of the model. Equations governing liq-uid and vapor hydraulics have been adopted from Mackowiak’scompilation [26] on packed bed fluid dynamics. The reflux drumand the reboiler drum have been sized to have a residence timefor the liquid of approximately 5 min when the vessels are 50%full, based on the total amount of liquid entering or leaving thevessels. Not all of the hydrogen fed to the column will react dueto disturbances in the feed composition. However, hydrogen isan expensive resource and thus, almost all the unreacted hydro-gen is recycled as vapor outlet stream of the partial condenser.A recycle ratio of 0.99 has been used for the column. The equa-tions of the model as well as the nomenclature can be found inAppendix A.

3.2. Control structure

3.2.1. Selection and pairing of controlled and manipulatedvariables

The set of controlled variables and manipulated variables needto be identified, in order to design a control structure. A degreeof freedom analysis gives the following set of seven manipulatedvariables that can be used for control:

u =

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

D

V1

LN

FH2

Q1

QN

R

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(10)

When compared with (3), Eq. (10) has two additional manip-ulated variables: the reflux drum vapor stream flow rate V1, andthe fresh hydrogen feed flow rate FH2 . This is due to the pres-ence of very light gases such as hydrogen in the system whichhas a very low bubble point temperature. Condensing hydrogenis economically infeasible, which necessitates the need for a par-tial condenser with a liquid outlet stream and a vapor outlet

stream.

The first four manipulated variables of u are flow rates andhence, they are part of the control loops that regulate the inven-tory of the column. The influence of these variables on the

1 l of Process Control 24 (2014) 113–124

cp

pocmmaBnafaatsostttnsasptaec

(

cwsT

vvlrfl

18 V. Mahindrakar, J. Hahn / Journa

orresponding controlled variables is straightforward and theairing can be performed as follows:

(11)

Even though the objective of an RD column is to maintain theurity and conversion of the product streams, RD control is basedn temperature points instead of composition. This is becauseomposition analyzers are expensive to purchase and have highaintenance costs [47]. They also introduce a delay in measure-ents if chromatographic methods are used. Temperature sensors

re inexpensive, reliable and introduce small measurement lags.ased on a degrees of freedom analysis, three temperature pointseed to be selected for the remaining three manipulated vari-bles. One of these control points should be somewhere above theeed and one should be somewhere below the feed. One temper-ture control point is selected at the top of the column to have

measurement related to the top product that is located abovehe reactive zone. Another of the temperature measurements iselected approximately halfway between the feed and the bottomf the column. Since the feed is at stage 30, a temperature mea-urement at stage 55 is a reasonable choice and has been foundo be sensitive to changes in the manipulated variables. A thirdemperature control point needs to be fixed at some point withinhe column. Hori and Skogestad [46] and Luyben [47] have listed aumber of criteria for selecting the tray at which a temperature sen-or should be placed for column control. Conventional techniquesre based, among others, on the slope of the temperature profile,ensitivity to changes in manipulated variables, SVD analysis, tem-erature invariance with changes in feed composition. However,he temperature profile in the reactive zone of the column mayffect the outcomes of these techniques. Therefore a more gen-ral approach has been adopted here for selecting the temperatureontrol tray. The following three criteria have been used:

(i) Avoid trays near the feed tray: the temperature profile nearthe feed tray is generally influenced by the enthalpy of thefeed to the column and may not be as sensitive to changes inthe manipulated variable.

(ii) Avoid trays near the top or the bottom of the column: sincethe distillate temperature and one temperature measurementbelow the feed have already been used as controlled variables,any temperature measurement near the top or bottom will behighly correlated with already selected measurements.

iii) Avoid the catalyst zone: reactions occurring in the catalystzone are exothermic and this affects the temperature of the cat-alyst stages. A temperature control point should not be selectedin this zone because the temperature is affected by reactionkinetics in addition to the regular dynamics due to separation.

Based on these criteria the third temperature control point washosen to be between the catalyst zone and the feed state. Stage 19as considered to be a good temperature control point and showed

ignificant sensitivity to step changes in the manipulated variables.hus, T19 was chosen as the third controlled variable.

The pairing of the remaining manipulated variables was doneia RGA analysis. Step input changes were given to the manipulatedariables of the model with some of the control loops open. Control

oops corresponding to the controlled variables liquid distillate (D),eflux drum vapor flow (V1), bottom flow (LN), and fresh hydrogeneed (FH2 ) are closed for determining the gain matrix. Simu-ated data obtained from this model involving partially open-loop

Fig. 3. Schematic of feedback and feedforward control structure for the RD column.

control was fitted to transfer functions which were estimated usingthe MATLAB system identification toolbox. Most of the responseswere fitted to first order plus time delay (FOPTD) transfer func-tions. Some of the responses were fitted to second order transferfunctions in order to obtain a better fit and some of these responsesalso included a lead term. Table 2 shows the computed transferfunctions in response to step changes in the manipulated variables.

Based on these transfer functions, the RGA was determinedfor the nominal operating conditions (feed benzene concentra-tion = 6 vol%). The RGA was also computed for the RD column at theextreme operating conditions, i.e., when the feed benzene concen-trations are 3 vol% and 11 vol%, since it is possible that the pairingmay change at different operating conditions. These results havebeen presented in Table 3 and it can be seen that the pairing of thecontrolled and manipulated variables is unaffected by the investi-gated changes in operating conditions.

Based on RGA computed at the three operating conditions andthe discussion above, the pairing of manipulated and controlledvariables results in the following:

(12)

Fig. 3 gives a schematic of the control structure used for thecolumn.

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124 119

Table 2Open loop transfer functions.

R QN Q1

T1−36.523(1 + 9632.8 s)

1 + 2(0.901)(3548.8) s + (3548.8 s)2

1.165 × 10−4(1 + 6052.2 s)

1 + 2(0.815)(3850.5 s) + (3850.5 s)2

1.0684 × 10−4

1 + 1887.1 s

T19−15.972

1 + 4564.7 s2.524 × 10−5

1 + 5817.4 s1.8704 × 10−5

(1 + 4555.3 s)(1 + 1834.3 s)

T55−10.502

1 + 3593.3 s1.4123 × 10−5

(1 + 3081.3 s)(1 + 2259.4 s)1.210 × 10−5

1 + 2(0.923)(3013.9) s + (3013.9 s)2

Table 3RGA for RD column at different feed benzene concentrations of (a) 6 vol%, (b) 3 vol%, and (c) 11 vol%.

(a) Feed benzene concentration of 6 vol% (b) Feed benzene concentration of 3 vol% (c) Feed benzene concentration of 11 vol%

R QN Q1 R QN Q1 R QN Q1

3

uTtflhvmttttulfw

G

wrppadrtoad

wt

3

Asfa4a

T1 −0.643 −0.157 1.800 −0.908

T19 −0.676 7.322 −5.646 −0.214

T55 2.319 −6.165 4.846 2.122

.2.2. Feedback controller designBoth the reflux drum and reboiler drum need controllers to reg-

late the flows and maintain specified liquid levels in the vessels.he reflux drum also holds vapor which needs to be regulated suchhat the pressure of the column is maintained. Since the streamow rates regulate the inventory of the column, P-only controllersave been used. These three proportional controllers were tunedia Ziegler Nichols tuning relations. A PI controller was used foraintaining the reflux drum outlet vapor flow rate V1 in order

o avoid an offset in the column pressure at the top (P1). PI con-rollers were also used for the temperature point control loops. Allhe PI controllers were tuned using internal model control (IMC)uning relations [41]. The transfer functions shown in Table 2 weresed to compute the controller parameters for temperature control

oops. A transfer function (13) was obtained for the fresh hydrogeneed (FH2 ) control loop by passing step change inputs to the modelithout the recycle stream.

Pwithout recycle= V1

FH2

= 75.2651 + 678.4 s

(13)

An IMC controller was designed based on transfer function (13)hich was determined for the distillation column without the

ecycle loop in accordance with design procedure described forlant-wide control [38–40]. Table 4 shows the controller tuningarameters that were derived and used for the control loops oper-ting on the model. The values of c were chosen by adjusting theesired speed of the closed-loop response. The faster the desiredesponse, the lower the value of c. As faster response can leado larger overshoots, c needs to be chosen to achieve a trade-ff between speed of response and potential for overshoot. Chiennd Fruehauf [48] have given the following general guideline toetermine acceptable values of c for FOPTD systems,

> c > (14)

here is the time delay. The values of c chosen for the PI con-rolled loops are listed in Table 4.

.3. Feedforward controller

Most conventional columns use feedback-only control [30].s reactive distillation columns can be viewed as an exten-ion of conventional columns, the first approach was to design a

eedback-only control structure, appropriately tune the controllers,nd observe the performance. However, as will be shown in Section, feed composition disturbances affect the column performancedversely, i.e., the product does not meet the specifications for

−0.026 1.933 −0.518 0.106 1.4126.596 −5.382 −0.234 5.307 −4.073

−5.570 4.449 1.752 −4.413 3.661

benzene concentrations for a significant period of time. As such itwas hypothesized that adding feedforward action to this structurewill improve the performance. The off-spec concentration of ben-zene in the product stream can be reduced if the flow of hydrogento the column is regulated according to the feed composition.Based on the disturbance variables, manipulated variables, andcontrolled variables, Gp and Gd from Eq. (8) are defined as follows:

Gp = V1

FH2

(15)

Gd = V1

zC6H6

(16)

These transfer functions were determined using the MATLABsystem identification toolbox on simulated data for open-loop stepresponses:

Gp = 99.391 + 3269.9 s

(17)

Gd = −7.457 × 104

1 + 3580.2 s(18)

In order to keep the process realistic, feedforward control withdifferent levels of measurement delay mf:

Gmf = e−mf s (19)

were used for the measurement transfer function. Also, since thefeedforward controller is represented by a lead-lag element, thecontroller transfer function was augmented with a filter with atime constant of 120 s in order to avoid large sudden changes inthe manipulated variable. The resulting dynamic feedforward con-troller is given by

Gf = 750.31 + 3269.9 s1 + 3580.2 s

11 + 120 s

(20)

If a static feedforward control law would be considered then thiswould result in

Gf = 750.3 (21)

Fig. 3 shows the control structure used for the column alongwith the feedforward controller for controlling the fresh hydrogenfeed.

120 V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124

Table 4Feedback controller settings.

Manipulated variable Controlled variable Kc i (s) c (s) Type of controller and tuning method used

Q1 T11.766 × 107

c1887.1 110 PI (IMC)

QN T192.305 × 108

c5817.4 582 PI (IMC)

R TN − 342.15c

3593.3 610 PI (IMC)

FH2 V19.013c

678.4 128.7 PI (IMC)

D h1 3340 – – P (Ziegler Nichols)LN hN 3830 – – P (Ziegler Nichols)V1 P1 −12.5 – – P (Ziegler Nichols)

Table 5Steady state results for inlet and outlet streams.

Stream Feed Fresh hydrogen Distillate Bottom Vent

Phase Liquid Vapor Liquid Liquid VaporTemperature (K) 430.0 430.0 293.5 495.5 293.5Pressure (kPa abs) 797.0 797.0 792.4 801.0 792.4Total flow rate (mol s−1) 265.0 65.9 85.4 180.0 3.0

Component Mole fraction

n-Butane C4H10 1.26E−02 – 3.87E−02 1.85E−28 1.31E−02n-Pentane C5H12 9.61E−02 – 2.97E−01 1.32E−17 2.35E−022,3-Dimethylpentane C7H16 1.16E−02 – 3.58E−02 2.59E−11 1.32E−033-Methylpentane C6H14 5.87E−02 – 1.82E−01 1.32E−09 5.33E−03n-Hexane C6H14 3.50E−02 – 1.08E−01 9.37E−09 2.56E−03Benzene C6H6 8.26E−02 – 1.09E−02 2.74E−05 2.14E−04Cyclohexane C6H12 – – 2.45E−01 6.26E−05 4.19E−033-Methylhexane C7H16 2.33E−02 – 1.54E−02 2.70E−02 1.63E−042,4-Dimethylpentane C7H16 2.34E−02 – 5.92E−02 6.27E−03 8.34E−04n-Heptane C7H16 9.77E−03 – 6.48E−05 1.43E−02 5.08E−07Toluene C7H8 2.81E−01 – 8.86E−07 4.14E−01 4.84E−09m-Xylene C8H10 2.06E−01 – 5.20E−14 3.04E−01 8.68E−17Cumene C9H12 1.59E−01 – 8.42E−18 2.35E−01 8.09E−21Hydrogen H2 – 1.00E+00 7.10E−03 0.00E+00 9.49E−01

4s

4

sm(bv

a

Methylcyclohexane C7H14 – –

Benzene conc. (vol%) 6.010 –

. Investigation and comparison of different controlchemes for the column

.1. Steady state results

The RD column model is assumed to initially operate at the sameteady state for any of the comparisons of different control schemesade in this section. This steady state corresponds to nominal feed

composition and temperature) being fed to the column, where theenzene concentration is 6 vol%. Table 5 includes the steady state

alues of all feed and product streams.

Fig. 4 depicts the profile of benzene and toluene concentrationt steady state in the column. The objective of the RD column is to

10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

Stage number

Mol

e fra

ctio

n

Benzene molfractionToluene molfraction

CatalystZone

Fig. 4. Profiles of benzene and toluene in RD column.

6.09E−06 1.88E−04 5.04E−08

0.251 (combined) –

react as much benzene as possible while minimizing the amountof toluene entering the stage containing catalysts packing. It can beseen that the benzene mole fraction increases along the height ofthe column, until the reactive zone, where it decreases due to thereaction. Very little toluene is present in the catalyst zone of theRD column and as a result 99.8% of the toluene from the reformatestream is retained in the bottom stream.

4.2. Feedback controller results

The rigorous model built in gPROMS was augmented with thecontrol structure shown in Fig. 3. The controllers specified in Table 4were used for investigation. The model combined with the con-trollers was subjected to changes in the inputs, representing stepdisturbances that occur after 1hr, to evaluate the performance ofthe control schemes. The set-points of all the controlled variablesremain unchanged throughout this investigation resulting in a reg-ulatory control problem.

Fig. 5 depicts the benzene concentration in the product for thecolumn under feedback-only control subjected to step changes inthe temperature of ±5 K (Fig. 5(a)) and the feed flow rate of ±5%(Fig. 5(b)). The responses indicate that the effect of the disturbanceson the product benzene concentration is not significant, i.e., onlysmall changes can be seen in the benzene concentration and the

concentration stays far below the allowable limit.

One of most common disturbances for the benzene hydrogena-tion process is a change in the feed composition. The benzeneconcentration in the reformate stream can increase up to a value

V. Mahindrakar, J. Hahn / Journal of Process Control 24 (2014) 113–124 121

a) b)

0 5 10 15

0.245

0.25

0.255

0.26

Ben

zene

vol

%

Feed temper ature -5 KFeed temper ature +5K

0 5 10 15

0.24

0.25

0.26

0.27

Ben

zene

vol

%

Feed flowrate +5%Feed flowrate -5 %

a) fee

owaprmTHsscc

4s

io

Fd

Time (hours)

Fig. 5. Responses to step changes in (

f 11 vol% [4]. In order to evaluate such a scenario, a step changeas given to the feed benzene composition from 6 vol% to 11 vol%

nd the concentrations of all other components were reduced pro-ortionally. The graphs in Fig. 6 labeled “feedback-only” show theesponses of the outlet benzene concentration and of the otheranipulated variables for a step change in the feed concentration.

he steady state benzene concentration meets the specifications.owever, it can be seen that the responses have significant over-

hoot and also a large settling time under a feedback-only controlcheme. This situation presents a clear opportunity for feedforwardontrol in order to minimize the effect of the disturbance on theontrolled variable.

.3. Comparison of feedback and feedforward/feedback controlchemes

The simulations shown in Fig. 6 for feedback-only controlnvolve significant overshoot and as a result a considerable amountf product does not meet the EPA specifications of 0.62 vol% [2] for

ig. 6. Responses of controlled and manipulated variables for step change in feed composiuty – Q1, (d) reboiler duty – QN , and (e) reflux ratio – R.

Time (hours)

d temperature and (b) feed flow rate.

the benzene concentration. Use of feedforward control can reducethe overshoot and settling time. All subfigures in Fig. 6 include acomparison of the responses of the column for feedback-only con-trol and feedforward–feedback control to a step disturbance in thefeed composition from 6 vol% to 11 vol% benzene. It can be clearlyseen that there is significant improvement in the response timeand the overshoot when feedforward control is added to the exist-ing feedback control scheme. Additionally, the trajectories of allmanipulated variables also remain within reasonable bounds forfeedforward–feedback regulatory control.

While Fig. 6 shows the positive impact that the addition of feed-forward control can have on the process, the simulation assumedthat concentration measurements are available instantaneously.This is not a very realistic assumption in practice unless an onlineanalyzer is used. One commonly used alternative is that samples

from streams are taken and then analyzed in a lab, i.e., measure-ments will only be available at discrete points in time and witha certain time delay. As such, it is important to know how muchof an effect measurement time delay has on the performance of

tion: (a) benzene concentration of the product, (b) fresh H2 feed – FH2 , (c) condenser

122 V. Mahindrakar, J. Hahn / Journal of Pro

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.2

0.4

0.6

0.8

1

Time (hours)

Ben

zene

vol

%

Feedba ck-onlyFF-FB with continuous measu rementsFF-FB with sampling time of 15 minFF-FB with sampling time of 30 minFF-FB with sampling time of 45 minFF-FB with sampling time of 60 min

Ff3

tbftsAs

ncmq0

D

w

H

fbanbc

TDs

ig. 7. Response to step change in feed composition for feedback-only control andeedforward–feedback control for five different sampling times (continuous, 15 min,0 min, 45 min, 60 min).

he feedforward–feedback (FF–FB) control system. This case haseen analyzed next. Fig. 7 shows a comparison of the responses foreedback-only control and combined feedforward–feedback con-rol where the disturbance measurement transfer function Gmf useseveral different time delays corresponding to the sampling times.s before, the step change disturbance occurs after an hour and theystem is initially at steady state.

It can be clearly seen that longer measurement time delays sig-ificantly degrade the advantages that the addition of feedforwardontrol has on the performance. In order to quantify the perfor-ance of the responses shown in Fig. 7, a measure is defined to

uantify the area between the curve and the EPA specification of.62 vol% [2]:

ev =∫ ∞

0

H(Bz vol% − 0.62) × (Bz vol% − 0.62) dt (22)

here H is the Heaviside function defined as

(x) ={

0, x < 0

1, x ≥ 0(23)

Table 6 shows a comparison of the deviation value computedrom Eq. (22) for different sampling times. Not surprisingly, it cane concluded that feedforward control reduces the upset condition,

s measured by Eq. (22), for all investigated cases. Similarly, it is alsoot surprising that the best performance is achieved for the com-ined feedforward–feedback control structure that uses an onlineomposition analyzer. However, the largest benzene concentration

able 6eviations, as measured by Eq. (22), for (a) dynamic feedforward controllers and (b)

tatic feedforward controllers.

(a)

Control structure Dev % reduct. Max Bzvol%

Feedback-only 1074 0.85FF–FB with continuous measurements 423 61% 0.66FF–FB with sampling time of 15 min 559 48% 0.76FF–FB with sampling time of 30 min 756 30% 0.97FF–FB with sampling time of 45 min 874 19% 1.02FF–FB with sampling time of 60 min 917 15% 0.94

(b)

Control structure Dev % reduct. Max Bzvol%

Feedback-only 1074 0.85FF–FB with continuous measurements 444 59% 0.67FF–FB with sampling time of 15 min 543 49% 0.74FF–FB with sampling time of 30 min 756 30% 1.04FF–FB with sampling time of 45 min 888 17% 1.13FF–FB with sampling time of 60 min 939 13% 1.04

cess Control 24 (2014) 113–124

that is occurring at some point during the operation among all casesis not occurring for the feedback-only control scheme but insteadfor feedforward–feedback control with significant time delays. Itcan be clearly seen from Table 6 that the larger the time delay forthe composition measurement, the less of a benefit in the over-all reduction of the offspec product can be achieved. At the sametime, the largest deviations from the target are occurring for longmeasurement time delays. It is beyond the scope of this study toevaluate these responses for different design specifications. How-ever, in order to put the discussion of the performance for differentmeasurement delays into a more general perspective, it should bepointed out that the dominant time constant of the systems is equalto 1.6 h. It can be concluded that the feedforward–feedback schemeis superior to feedback-only control for the case of continuous mea-surements or measurements with a time delay of up to 15 min,which corresponds to 15% of the dominant time constant. There isonly a marginal benefit to the feedforward–feedback scheme if thetime delay is 30 min, corresponding to 31% of the dominant timeconstant, and it is questionable if there are any benefits of includ-ing feedforward control if the measurement time delay is 45 minor more, corresponding to 46% of the dominant time constant.

In addition to investigating a dynamic feedforward controller, astatic feedforward controller has also been investigated. Table 6bshows a comparison of the deviation values computed using thestatic feedforward controller given by Eq. (21) instead of thedynamic feedforward controller from Eq. (20). The results are closeto those obtained by using a dynamic feedforward controller. Infact, the graphs of the responses overlap with those depicted inFig. 7 for dynamic feedforward control and as such no separate fig-ure for the graphs is included. Thus, from an application point ofview, a simple static feedforward controller could be used insteadof a dynamic feedforward controller without significant loss of per-formance.

One last point to consider is that this investigation focused onstep disturbances as these are the most common disturbances forthe scenario investigated in this work. As such, it was appropriateto model the measurements occurring from lab samples as contin-uous samples with a time delay instead of using discrete sampleswith time delays as the two will return identical results for stepdisturbances. However, it should be pointed out that if the benzeneconcentration disturbances would have had a different nature thana step, that it would have been required to use discrete samplingand time delays. This was not necessary for the cases investigatedin this work, though.

It was one of the goals of this investigation to determine thebenefit of using a control scheme that combines feedforward andfeedback control over a feedback-only control scheme. The simu-lation results indicate that a significant benefit only exists if upsetsin the feed composition can be quickly detected.

5. Conclusions

Benzene hydrogenation via reactive distillation is a processthat has found significant use in the process industries. However,no models of this process can be found in the open litera-ture. This paper addresses this point by developing a dynamicequilibrium-based model for a reactive distillation column usedfor the hydrogenation of benzene. Simulations were carried out todetermine transfer functions between manipulated and controlledvariables. Control loop pairing was performed using RGA analy-sis and the feedback controllers were tuned via IMC tuning (PI)and Ziegler Nichols tuning (P). a model-based feedforward con-

troller was also designed to reduce upset conditions caused bydisturbances.

Simulations indicate that the column performance for feed tem-perature and feed flow rate disturbances remains acceptable for

of Pro

anFffd

adact

A

f(

A

A

C

M

C

∑

V

x

E

0

P

P

M

C

∑

V

x

V. Mahindrakar, J. Hahn / Journal

feedback-only control scheme. However, the column has a sig-ificant settling time for disturbances in the feed composition.eedforward control can reduce these upset conditions resultingrom feed disturbances. However, it was shown that the use of aeedforward–feedback control scheme is only beneficial if the timeelay associated with the feed composition measurement is small.

In summary, this paper (1) presented the first detailed model of reactive distillation column for the hydrogenation of benzene, (2)esigned and evaluated a feedback control scheme for the column,nd (3) investigated the benefit of using a feedforward/feedbackontrol structure for different sampling times of the feed composi-ion measurement.

cknowledgment

The authors gratefully acknowledge partial financial supportrom the American Chemical Society - Petroleum Research FundGrant PRF# 50978-ND9).

ppendix A.

.1. Model

ondenser and reflux drum

ass balance

d(Ml1 + Mv1 )

dt= V2 − L1 − D − V1 (A1)

omponent balances

d(Ml1x1,i + Mv1y1,i)

dt= V2y2,i − L1x1,i − V1y1,i ∀i : 1 to n − 1 (A2)

n

i=1

x1,i = 1;n∑i=1

y1,i = 1 (A3)

apor–liquid equilibrium

1,i�l1,i = y1,i�v1,i ∀i : 1 to n (A4)

nergy balance

= V2Hv2 − V1H0 + Q1 (A5)

d(Ml1Hl1 + Mv1Hv1 )

dt= V2H0 − (L1 + D)Hl1 − V1Hv1 (A6)

acked section

late j

ass balance

d(Mlj + Mvj )

dt= Vj+1 + Lj−1 − Vj − Lj + Ahj(HETP)�cat

n∑i=1

rxnj,i (A7)

omponent balances

d(Mlj xj,i + Mvj yj,i)

dt= Fjzj,i + Vj+1yj+1,i − Lj−1xj−1,i − Vjyj,i − Ljxj,i

+ Ahj(HETP)�catrxnj,i ∀i : 1 to n − 1 (A8)

n

xj,i = 1;n∑yj,i = 1 (A9)

i=1 i=1

apor–liquid equilibrium and Murphree efficiency

j,i�lj,i = y∗j,i�lj,i ∀i : 1 to n (A10)

cess Control 24 (2014) 113–124 123

yj,i = yj+1,i(1 − �) + y∗j,i� (A11)

Energy balance

d(MljHlj + MvjHvj )

dt= Vj+1Hj+1 + Lj−1Hlj−1

− LjHlj − VjHvj − Hrxn,j

(A12)

Flow rate and holdups

Liquid

Mjvollj = hj(HETP)A (A13)

hj = 0.34a1/3u2/3j

(A14)

Vapor

PjA(HETP)(ε − hj) = Mvj RgasTj (A15)

�P0,j

HETP=

(1 − ε)ε3

u2v�v

dpK(A16)

= 150Rev

+ 1.75 (A17)

�Pj = �P0,j

[1 − 2hj

dpa

]−5

(A18)

Pj+1 = Pj + �Pj (A19)

Reaction rate

rxnj,Benzene = −kj,1KA1KH1CAj,1CHj

(3KA1CAj,1 + (KH1CHj )1/2 + 1)

3(A20)

rxnj,Toluene = −kj,2KA2KH2CAj,2CHj

(3KA2CAj,2 + (KH2CHj )1/2 + 1)

3(A21)

ki,j = ki,0 exp

[− EaRgas

(1Tj

− 1T0

)](A22)

Reboiler

Mass balance

d(MlN )

dt= LN−1 − LN − VN (A23)

Component balances

d(MlN xN,i)

dt= LN−1xN−1,i − LNxN,i − VNyN,i ∀i : 1 to n − 1 (A24)

n∑i=1

xN,i = 1 (A25)

Energy balance

d(MlNHlN )

dt= LN−1HlN−1

− (LN + VN)HlN (A26)

VNHlN − VNHvN + QN = 0 (A27)

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